How to swipe transparency?
With the boolean on the circle set to 'Difference' I did not find that the circle lost it's material:



Note: Make sure that he circle has some volume so it isn't completely flat. Select all the faces of the circle and use 'Extrude' (E) to give the circle some volume.

The cube that is used as the masking object can then be set to not render by selecting it and pressing Ctrl+H. 

Resulting in: